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H. David Sherman 

Sloan School of Management 

Massachusetts Insitute of Technology 

Revised October 1983 

SSM Working Paper #1498-83 196-^ 







H. David Sherman 

Sloan School of Management 

Massachusetts Insitute of Technology 

Revised October 1983 

SSM Working Paper #1498-83 i%3 

How can a manager evaluate the productivity of a bank branch, a 
hospital, or other service organization? A bank branch may have outstanding 
profit performance based on a measure of the revenues earned on funds less 
the costs of funds generated, and less the operating costs. This measure 
does not, however. Indicate whether the branch Is using Its resources 
efficiently or whether It could reduce Its operating costs and further 
Increase profitability. Similarly, If one hospital provides patient care at 
a cost of $300 per day and another provides patient care at $350 per day, 
can a manager draw any conclusions about their relative productivity without 
further considering the mix and nature of patient care provided? Measuring 
the productivity of these and other service businesses requires techniques 
that are more sensitive than accounting and ratio type measures and which 
can explicitly consider the mix of service outputs produced. This article 
explains how to apply a recently developed method for measuring and 
improving the efficiency of service businesses. The technique, referred to 
as Date Envelopment Analysis, has thus far been applied to banks, hospitals, 
computer manufacturer field service organizations, and educational 
institutions, as well as other service organizations. 


The service sector of the U.S. economy has been estimated to account for 

over 60% of Gross National Product and employment. Add to this the service 

components of manufacturing firms and it is clear that service sector 

productivity is a substantive issue as suggested in the following examples. 

• Over 20% of computer manufacturer revenues are generated from 

customer service activities. These companies need to monitor and 
manage the service aspect of their business to help achieve their 
growth and profitability goals. 

• Hospital cost Increases are a serious and continuing concern. 
Their management are Increasingly accountable for assuring 
efficient delivery of health care services. 

• Public sector organizations face continued taxpayer pressures to 
maintain service at or above current levels but at a lower cost. 

Although the need for managerial methods to enhance productivity in the 
service industry Is apparent, techniques to accomplish these Improvements 
have not been developed as they have for the manufacturing sector. 

Service business efficiency is often more difficult to evaluate than 
manufacturing business efficiency because the efficient amount of resources 
required to produce service outputs is difficult to determine. The standard 
or efficient cost of a manufactured product can generally be determined with 
some precision. This manufacturing standard can be used to identify 
operating inefficiencies by analyzing differences between actual cost and 
standard costs through classical cost accounting variance analyses. (1) 
Service organizations have not generally developed standard cost estimates 
of outputs. One reason for this is that the specific resources required to 
provide a specific service output are difficult to identify. (This, of 
course, is also true of manufacturing organizations that produce highly 
customized products.) Another reason may be that those being evaluated 
against a standard cost would not accept or be able to agree on a standard 
because of the professional judgement involved in providing each type of 
service. For example, the professional might convincingly argue that no two 
audits, heart operations, or customer service calls are alike, so that no 
standard or efficient input level can be identified as a basis for 
evaluating the efficiency of producing such services. 

Another approach to evaluate service productivity is to develop a series 
of output to input ratios such as full-time equivalents per service unit. 

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dollars per transaction, etc. The Idea Is that units with higher costs per 
transaction would be potentially less efficient than those with lower 
costs. For example, a measure of bank branch operating efficiency that 
might be used Is the ratio of cost per teller transaction. The branch with 
the higher cost per teller transaction may be less efficient. 
Alternatively, this higher cost per transaction may be due to a more complex 
mix of transactions. That Is, a branch which primarily opens new accounts 
and sells certificates of deposit would require more resources per 
transaction than another branch that primarily processes less complex 
transactions such as deposits and check cashing. In short, the problem with 
these ratio measures is that the mix of outputs is not explicitly considered. 

Profitability, return on investment, and other financial ratios are 
highly relevant as performance measures of many service businesses, but they 
are not sufficient to evaluate operating efficiency. For example, a bank 
branch may be profitable when profit reflects the Interest and the revenues 
earned on funds generated by a branch less the cost of these funds and less 
the costs of operating the branch. This profit measure does not, however. 
Indicate whether the resources used to provide customer services are being 
managed efficiently. The branch that processes a high proportion of cash 
withdrawals and other non-fund-generating services may have higher operating 
costs and lower profitability than one which processes a lower proportion of 
nonfund generating transactions. Nevertheless, the less profitable branch 
may be more efficient using its personnel and other Inputs than the more 
profitable branch. In this Instance, the more profitable branch may be able 
to provide its same service level with fewer inputs which would result in 
lower operating costs and yet greater profitability. For non-profit 
organizations, profit maximization Is generally a secondary consideration 

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and the need for other types of performance measures Is even more acute than 
In the for-profit service businesses. 

There are also differences within the service sector organizations that 
need to be considered in adopting performance evaluation techniques. 
Professional service organizations, such health care, management consulting, 
and accounting firms experience greater difficulty defining efficient 
input/output relationships than other types of service organizations where 
labor inputs are highly controlled and standardized, such as fast food 
restaurants. This is most evident when one examines a text on operations 
management in service businesses (see for example [2]). The management 
techniques that are described in such a text tend to be extremely useful in 
managing a McDonald's restaurant but are of only marginal value in running a 
health care clinic. In contrast, texts discussing management of nonprofit 
service organizations such as [3] reflect keen awareness of the difficulty 
of measuring outputs and determining the efficient level of inputs required; 
however, solutions to these problems are not provided in any detail. 

Recently, a new technique was developed which has the ability to compare 
the efficiency of similar service organizations by explicitly considering 
their use of multiple Inputs (resources) to produce multiple outputs 
(services). The technique, referred to as Data Envelopment Analysis (DEA) , 
circumvents the need to develop standard costs for each service provided. 
It provides a measure of efficiency that is explicitly sensitive to the 
output mix and is consequently more comprehensive and reliable than use of a 
set of operating ratios and profit measures. Data Envelopment Analysis 
compares a set of service organizations and identifies units that are 
relatively inefficient, the magnitude of the inefficiency, and alternative 
paths to reduce the identified inefficiencies. Management can use DEA to 
Identify the inefficient units and the magnitude of the inefficiency. In 

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addition, DEA can help assess plans to remedy and reduce these 
inefficiencies. This can lead to (1) a reduction In the cost of operations 
or (2) an increase in the services provided without an increase in the level 
of resources utilized by the inefficient units* 

DEA is a linear programming technique originally developed by Charnes, 
Cooper, and Rhodes ([4], [5], and [6]) to evaluate nonprofit and public 
sector organizations and has subsequently been found to be a valuable tool 
in application to a variety of corporate service type organizations. DEA 
has been applied to hospitals [7], primary and secondary educational 
Institutions [6j, [8], court systems [9], armed forces recruiting offices, 
bank branches [10], and customer service offices of a computer manufacturer. 

The following section briefly describes and Illustrates how DEA works. 
The appendix provides details about how DEA can be applied using any 
standard linear programming package. The subsequent section describes how 
this has been applied to hospitals and bank branches. The final section 
discusses the strengths and limitations of DEA and how management can use 
DEA to evaluate and Improve operating efficiency of service organizations. 

Data Envelopment Analysis - How it Works and How to Interpret the Results 

Use of DEA to evaluate efficiency will be illustrated with a simplified 
bank branch example where there is only one type of transaction processed 
and two types of resources used to processes these transactions - bank 
tellers and supplies. This example was selected because it lends itself to 
an easily visualized graphic description. In addition, this example is 
simple enough to be analyzed without DEA, so that the results can be 
compared to an independent analysis of efficiency. Note that DEA is most 
valuable in complex situations where (1) there are multiple outputs and 

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Inputs that cannot readily analyzed with other techniques like ratios, and 
(2) where the number of service organization units being evaluated are so 
numerous that management cannot afford to evaluate each unit In depth. For 
example, an actual bank application Included 18 different transaction types 
as output measures and 14 branches were to be evaluated. DEA was used to 
help direct management's efforts to Improve efficiency of units that were 
first identified as inefficient with this technique. 

Assume that there are five bank branches (Bl, B2, B3, B4, and B5) that 
each process 1,000 transactions such as deposits by jointly using two 
inputs, tellers measured in labor hours (H) and supplies measured in dollars 
(S) during one common time period (week, month, year, etc.). The amount of 
inputs are summarized in table 1. 

































The problem facing the manager is to identify which of these branches are 
inefficient and the magnitude of the inefficiency. This Information could 
be used to locate the branches that require remedial management action, to 
reward the more efficient managers, and/or to determine the management 
techniques that are used in the more efficient branches so that they can be 
transferred to less efficient branches to Improve their operating 
efficiency. While the manager can observe the number of transactions 
processed and the amount of resources (H and S) used, the manager does not 

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know the efficient output/input relationship. That is, the efficient amount 
of labor and supplies needed for each transaction is not readily 
determinable. Hence, the problem might be visualized as in Figure 1. 

In this example, it can be observed that Bl and B2 are relatively 
inefficient. Bl produced the same output level as B4 but used 100 more 
supply dollars (S) than were used by B4. B2 also produced the same output 
level as B4 but achieved this through the use of 10 more Teller labor 
hours. With the information available in table 1, it is not possible to 
determine whether B3, B4 or B5 are more or less efficient. While 
information about relative prices might allow one to rank B3, B4 and B5, the 
finding that Bl and B2 are inefficient would not change. That is, Bl and B2 
should be able to reduce inputs without reducing outputs regardless of the 
price of the inputs. 

Data Envelopment Analysis compares each service unit with all the other 
service units and identifies those units that are operating inefficiently 
compared with other units' actual operating results. It accomplishes this 
by locating the best practice units, (units that are not less efficient than 
other units being evaluated) and measures the magnitude of inefficiency 
compared to the best practice units. The best practice units are relatively 
efficient and are Identified by a DEA efficiency rating of E = 100%. The 
inefficient units are identified by an efficiency rating of less that 10 0% 
(E < 100%). 

The DEA techniques and the data needed to apply DEA are described in 
Exhibit I. DEA is applied to the example in Table 1 in Exhibit I. 

DEA first provides the type of information summarized in table 2. 

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Figure 1 

Problem: Which are the inefficient branches and what is the magnitude 

of the inefficiency present? 




20 units of H 
300 units of S 





1000 transaction 


30 units of H 
200 units of S 

1000 transaction 


40 units of H 
100 units of S 

1000 transaction 


20 units of H 

200 units of S 

]000 transaction 


10 units of H 
400 units of S 

1000 transaction 

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Table 2 























Table 2 Indicates that DEA Identified the same inefficient branches 
that were identifiable through observation of the data. Bl and B2 have 
efficiency ratings below 100% which identifies them as inefficient. In 
addition, DEA further focuses the managers attention to a subgroup of the 
bank branches which are referred to as the efficiency reference set in Table 
2. This efficiency reference set includes the group of service units 
against which each Inefficient branch was most directly found to be 
inefficient. For example, Bl was found to have operating Inefficiencies in 
direct comparison to B4 and B5. The value in parenthesis in Table 2 
represents the relative weight assigned to each efficiency reference set 
member to calculate the efficiency rating (E). (This corresponds to the 
non-zero shadow prices of the constraints which is directly available from 
the DEA linear program output.) More specific information about the nature 
and magnitude of the inefficiency present are available from the DEA results 
as is illustrated in Figure 2 using B2 as an example. 

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Figure 2 

All branches produce 1000 units of a single transaction 
type (T) using the following amounts of Teller Hours (H) 
Supply Dollars (S) . 







J» B2 


y (25.7, 171) 


Teller Hours (T) 


DEA has determined that the relatively efficient bank branches among the 
five are B5, B4, and B3. This can be represented In this simple case by the 
solid line in Figure 2 which locates the units that used the least amount of 
inputs to produce their output level. DEA indicates that B2 is inefficient 
compared to the line connecting B4 and B3; B2 is 85.7% efficient compared to 
B4 and B3. This means that one way for B2 to become efficient is to reduce 
its inputs to 85.7% of its current level which would move B2 onto this 
relatively efficient production segment at point e in Figure 2, which 
reflects use of 25.7 teller hours (.857 X 30) and use of 171 supply dollars 
(.857 X 200). DEA provides information to complete the calculation 
suggested in Figure 2. This Is Illustrated in Table 3. 

Table 3 indicates that a mixture of operating techniques utilized by B3 
and B4 would result in a composite hypothetical branch that processes the 
same amount of transactions (1,000) processed by B2 but also requires fewer 
inputs than wejre used by B2. Hence, by adopting a mixture of the actual 
technique used by B3 and B4 , B2 should be able to reduce teller hours by 4,3 
units and supply dollars by 29 units without reduction in its output level. 
A similar calculation can be completed for each inefficient unit located via 
a DEA analysis. 

Management is also provided with alternative paths to Improve efficiency 
of B2. One path suggested in Table 3 is for B2 to reduce H by 4.3 units and 
reduce S by 29 units. Other paths are ascertainable from the DEA output as 
follows: DEA calculates a relative value for each input and output (the 
v^ and V2 values that result in the efficiency rating as noted in 
Exhibit I). For branch Bl, this value is 1.436 for teller hours (H) and 
0.286 for supply dollars (S). This means that for each unit of reduced 
teller hours, the efficiency of B2 increases by 1.43%; and for each unit 

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Table 3 








Teller Hours 

Supply Dollars 

(.2857) X 1000 + (.7lA3)x 1000 








The composite for B2 can then be compared with the Inefficient unit B2 
as follows: 
















A. 3 






Used by 
Branch B2 

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decrease In supply dollars, the efficiency of B2 will Increase by 0.286%. 
For B2 to become relatively efficient, it must increase its efficiency 
rating by 14.3percentage points. Hence, B2 can become efficient by 
decreasing H by 10 hours (10 hours X 1.43% = 14.3%) or by decreasing S by 50 
units (50 X 0.286% = 14.3%) or by some combination of these reductions in H 
and S. The choice of which path to follow would, of course, be based on 
management's evaluation with respect to cost, practicality, and feasibility 
under the particular organization's circumstances. 

At this point it must be reemphasized that DEA results are most useful 
when there are multiple outputs and inputs and where the type of intuitive 
analysis that could be applied to verify the DEA results in the above 
example would not be possible. Nevertheless, the efficiency rating, the 
efficiency reference set, the analysis as performed in Table 3, and the 
ability to determine alternative paths that would make an inefficient unit 
efficient would all be readily available. 

How Can A General Manager Understand All This Technical Material? 

Business application of DEA to banks, hospitals, and customer service 

organizations suggests that the presentation along the lines of Table 3 is 

one of the most direct ways to summarize and explain what DEA has achieved 

and the implications to management. The interpretations of DEA results tend 

to proceed in the following order: 

• The efficiency ratings are generated as in Table 2. Units that are 
efficient (E = 100%) are relatively and not strictly efficient. 
This means that there is no other unit that is clearly operating 
more efficiently than this unit but it is possible that all units 
including these relatively efficient units can be more efficiently 
operated. The efficient branches, B3, B4, and B5, therefore, 
represent the best practice but not necessarily the best possible 
management practice. 

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Inefficient units are located with efficiency rating of 
E < 100%. These units, Bl and B2, are strictly Inefficient 
compared to all the other units and are the ones where remedial 
action by management should be considered. In fact, the 
inefficiency identified with DEA will tend to understate rather 
than overstate the inefficiency present. 

The efficiency reference set indicates the relatively efficient 
units against which the inefficient units were most clearly 
determined to be inefficient. The presentation In Table 3 
summarizes the magnitude of the inefficiencies located by comparing 
the inefficient unit with its efficiency reference set. 

The results in Table 3 might be summarized as follows: 

32 has been found to be relatively less efficient than a composite 
of the actual output and input levels of B3 and B4. If a 
combination of operating techniques used in B3 and B4 were 
transferred to inefficient unit B2 , B2 should be able to reduce the 
amount of H used by 4.3 units and reduce the amount of S used by 29 
units while providing the same level of services. Other methods to 
Improve efficiency are also identifiable via DEA, such as were 
described above, which should also be considered by management in 
designing a program to improve the efficiency of each inefficient 
unit Identified by DEA. 

Table 4 

Comparison of Teaching Hospitals' Medical Surgical (MS) Area 



Set CERS) 

Area Cost Per 
Patient Day 











A, C, E 













^34. 29 


1 Deviation 

$ 4.27 


- 14 - 

Application and Use of PEA as Management Control Tool 
to Improve Operating Efficiency 

Hospital Application 

A set of teaching hospitals were compared and evaluated using DEA. The 
Inputs were Identified as bed days available, full-time equivalents of 
non-physic Ian staff, and supply dollars. Outputs Included measures of 
number of Interns, residents and nurses trained and the number of bed days 
of care administered for each patient type. 

The DEA results located a set of Inefficient hopsltals not otherwise 
Identifiable using ratio analysis techniques (e.g., cost per day, cost per 
patient), the method used by the local regulatory agency which needs this 
type of data to affect hospital reimbursement rates. The DEA results were 
found to be meaningful and accurate by a panel of hospital experts familiar 
with these hospitals. Moreover, management of one inefficient hospital 
acknowledged the inefficiencies identified with DEA particularly with 
respect to their use of excessive personnel and bed days. 

The DEA results focusing on the medical/surgical areas of a group of 
these hospitals are in table A along with the ratios of cost per patient day 
of care. The cost per patient day is a typical example of ratio which might 
be used to locate high and low cost hospitals. Note that there is no 
objective means of establishing a cutoff cost level which separates the more 
and less efficient hospitals. The local regulatory agency defined 
potentially inefficient hospitals as those which have costs over one 
standard deviation above the mean. This "rule of thumb" identifies only 
hospital C as inefficient. In addition, there is no way to determine if 
this represents use of excess inputs or payment of higher prices for their 
inputs. In addition, hospital C may have higher costs primarily because it 

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treats more complex patient Illness or provides greater amounts of teaching 
services. These are typical problems associated with financial and 
operating ratios. 

DEA identified two hospitals, D and G, as inefficient in their use of 
inputs to produce the actual mix of patient care and teaching services 
provided. Note that these hospitals would have gone unnoticed using 
ratios. Unlike the ratios, the use of DEA allowed for explicit 
consideration of case mix and teaching outputs. DEA Identified the use of 
excess amounts of Inputs in specific hospitals without the need for an 
arbitrary or subjective decision rule as to which units are inefficient. 
Correcting these inefficiencies would result in yet lower costs for 
hospitals D and G. 

Management of hospital D studied the detailed DEA results and agreed 
that they had an excessive number of beds and personnel compared with the 
other hospitals. They planned to reduce the number of beds by 19, freeing 
up space for other uses. They also determined that personnel levels were 
excessive by 5.4 full-time equivalents but chose not to make any reductions 
here because their policy was to maintain high personnel levels to provide 
more personalized care. The planned reduction in the number of beds was 
reevaluated using DEA. This indicated that this hospital would still be 
rated as inefficient but with a higher rating of 96% compared with the 
original level of 88%. If they also reduced personnel by the 5.4 units they 
identified, their DEA efficiency rating would have increased to 100. 

Hence, DEA provided a basis for improving productivity by reducing the 
number of beds and it indicated reduction in personnel were possible without 
affecting output levels which could further reduce costs. In this case, DEA 
also helped to clarify the cost of the intended inefficiency or slack and 
challenges management to justify this cost. Thus, DEA provided insights 

- 16 - 

about Inefficiencies not available from ratio analysis. Nevertheless, the 
questions raised about the cost per patient day and other similar ratios are 
also relevant. Hence, DEA is a complement to, rather than a substitute for, 
other types of analysis. 

Savings Bank Application 

Branches of a savings bank were compared using DEA to assess their 
operating efficiency. The bank's head office management developed a branch 
profit measure which was considered to be useful in evaluating a number of 
dimensions of branch performance. This profit measure did not, however, 
provide information about branch resource utilization because the 
transaction mix was not considered and the profit was mostly a measure of 
earnings from funds generated by each branch. Hence, the potential benefits 
of applying DEA were of interest. The process began by identifying relevant 
outputs and inputs of a branch. Inputs included personnel full-time 
equivalents and supply costs. Outputs were identified as the number of each 
of seventeen transaction types, including for example, opening new accounts, 
withdrawals, deposits and issuing savings bonds. 

DEA was first used to identify inefficient branches and the magnitude of 
input reductions that were possible. This result was not apparent from 
other evaluation techniques used in the bank including profitability 
measures and operating ratios such as cost per transaction and number of 
transactions per FTE. DEA indicated that six of the 14 branches were 
inefficient. Most of the branches identified as inefficient were consistent 
with head office management expectations based on their view of quality of 
the managers in these branches. However, one branch identified as 
inefficient was a complete surprise to management. This information was 
particularly useful because it quantified the operating inefficiencies which 

- 17 - 

were only vaguely apparent to management based on their Intuition about the 
branch managers. Moreover, this insight was obtained without the need to 
Involve branch managers in any part of the process, since the output and 
input data were already available at the head office. 

DEA first alerted management to the branches that were inefficient and 
the magnitude of the inefficiency. This allowed management to assess the 
potential benefits of taking remedial action. Beyond this, DEA specified 
the efficient branches against which the inefficient branches should be 
compared to understand and locate the source of the inefficiencies. By 
comparing the operating techniques in the narrowed set of efficient and 
inefficient branches, management could identify the techniques which require 
improvement and the techniques which should be transferred from the more 
efficient branches to the less efficient branches to improve the latter 's 

Use of DEA alerted management to cost saving opportunities that were not 
apparent with other techniques and it helped management to allocate their 
time and remedial efforts to areas where operating weaknesses were now known 
to exist. Based on favorable reaction to this effort, bank management 
further proposed to use DEA to compare their branches with those of another 
bank they were acquiring to determine if there were opportunities for 
improving operations through the transfer of good branch management 
techniques from the original to the newly acquired branches or vice versa . 

The above examples illustrate the use of DEA to compare organizations 
that jointly produce a set of similar service outputs with a set of inputs. 
This can readily be applied across organizations in the non-profit sector 
where data are publicly available as in the teaching hospital example. 

- 18 - 

Corporate applications of PEA will tend to emphasize cases where 
management wants to evaluate and Improve efficiency of a set of offices 
providing similar services as In the bank example . It would also be 
possible to compare Independent competing firms using DEA, but this type of 
data would generally be difficult to obtain due to the condlfentlallty of 
detailed operating data. Consequently, the corporate applications will 
generally be limited to comparison of multiple service offices such as bank 
branches, customer services officers, multi-office CPA firms, and Insurance 
claims offices. 

How Would Management Apply DEA 

Step 1 ; Management would Identify the units for which a DEA efficiency 
evaluation would be of interest. This would generally be a set of units 
that provide similar services for which management wants to evaluate 
performance and Improve operating efficiency. 

Step 2 ; The relevant outputs and inputs of the units to be evaluated 
would be identified by management and measured for a representative period 
of time (year, quarter, month). The relevant outputs are those services and 
other activities that the unit is responsible for to achieve its business 
purpose. The inputs are those resources that are required to produce the 
designated outputs. Field applications of DEA have indicated that this 
process of output and input indentlficatlon In itself is often useful to 
managers, as the outputs and Inputs are frequently not explicitly identified 
or understood. In addition, some of the relevant outputs and Inputs may not 
have been measured or captured In the management Information system of the 
firm. The absence of data on relevant outputs and Inputs has tended to 
raise questions about the adequacy of the information system, since this 
type of input-output data are needed to assess operating performance 

- 19 - 

regardless of the techniques that may be used. Generally, the outputs used 
should be related to the Inputs selected in that an efficient unit should be 
expected to respond over time to an increase or decrease in outputs with a 
corresponding increase or decrease in the various inputs. 

If all the relevant outputs and inputs are not included in the DEA 
analysis, the DEA results will have to be reviewed for any bias that might 
result. For example, the DEA application to hospitals excluded a measure of 
the quality of services. Such use of DEA requires that the results be 
reconsidered to determine if the inefficient hospitals' quality of care 
exceeds the efficient hospitals' quality of care by a large enough margin to 
compensate for the DEA calculated inefficiency. The hospital application 
that addressed this issue found that quality of care was not a compensating 
factor. Other applications of DEA may, however, require some qualification 
if certain relevant input or output measures are excluded. 

Step 3 : DEA would be applied to the output and input data and the 
results would be analyzed to help management locate and remedy operating 
inefficiencies. Generally, management will not have seen results similar to 
DEA and these results will tend to provide insights not available from other 
widely used analytical techniques such as ratio analysis. Management might 
begin by considering whether the location and magnitude of inefficiencies 
are consistent with their prior view of the operations of the service units 
being evaluated. This may raise questions about the completeness and 
representativeness of the output and input data. 

The inefficient units would then be further studied and compared with 
their efficiency reference set units to evaluate the cause and 
controllability of the identified inefficiencies. In some cases, the 
Inefficiencies present may represent intended slack built into a unit or 
special circumstances which do not permit improvements in operating 

- 20 - 

efficiency. In this circumstance, DEA helps to understand the cost of this 
Inefficiency and no further managerial actions may be warranted. When the 
inefficiencies are found to be associated with the systems and managerial 
techniques used in these units, remedial action to improve efficiency would 
be Implemented. 

Insights from DEA direct management's attention to aspects of operations 
which are highly likely to benefit from remedial action. In contrast to 
other techniques, DEA evaluates units by explicitly and simultaneously 
considering the multiple Inputs used to produce multiple outputs and without 
the need to know the efficient input/output relationships. Although DEA 
does not actually specify the remedial action needed, it narrows the focus 
of management's Investigation to the inefficient units and their efficiency 
reference set. Through this process, DEA helps allocate management support 
to areas where weaknesses are known to exist and helps management identify 
ways in which management techniques can and should be improved. 

Dynamic Analysis with DEA 

In addition to the static one year or period analysis such as was 
completed for the bank branches and hospitals, DEA can monitor and thereby 
help control the level of operating efficiency over time. DEA can be run 
with multiple period information (quarters, years, etc.) for individual 
ogranization units or for each of a set of units being compared to determine 
if units are becoming more or less efficient with respect to other units and 
with respect to themselves over time. The use of DEA for successive periods 
would suggest whether the previously inefficient units have become 
relatively efficient through remedial actions taken and DEA would help 
locate other units that have become relatively inefficient. 

- 21 - 

Sensitivity Analysis 

DEA suggests a variety of paths to reduce Identified inefficiencies. 
Management may find that yet other paths are more feasible and/ or less 
costly. DEA can be reapplied to the same set of units after adjusting the 
outputs and inputs to reflect management's plan to improve efficiency. DEA 
would indicate whether the changes anticipated will reduce the 
inefficiencies sufficiently for management purposes. 

What are the Costs of Using DEA? 

DEA can be run and interpreted with very modest amounts of training by 
individuals that have access to and are able to run any standard linear 
program package. Once the input and output data are available, the 
Incremental cost of obtaining a DEA evaluation Is minimal when such a linear 
program package is on hand. 

The costs of Identifying and collecting the output and input data not 
already available may be significant. While this cost might be incurred In 
conjunction with the DEA process, it is frequently considered valuable as an 
end in itself and is often an indicator of Infonnation gaps about aspects of 
operation which should be remedied regardless of the analytic techniques 
that will be used. 

The area where significant costs are Involved are in the followup to 
evaluate the way inefficiencies can be reduced and In identifying the 
techniques that exist In relatively efficient units that should be 
transferred to less efficient units. The value of DEA In this context is 
its ability to narrow management's focus to areas where inefficiencies are 
known to exist and where benefits of managerial action are likely to result 
In productivity Improvements. Hence, these costs are likely to lead to 
benefits which compensate for costs of the DEA process. 

- 22 - 

In summary, the class of service organization which can be evaluated 
using DEA are those which produce multiple services with multiple Inputs, 
where the efficient output/input relationships are not known or are 
difficult to Identify, and where several units can be compared to evaluate 
relative performance. For this class of service units, DEA is a useful 
technique for locating ways to Improve efficiency and profitability and can 
be a valuable complement to other management control tools and techniques 
used within these organizations. Considering the very few techniques 
available to evaluate and Improve service business productivity, it would be 
reasonable for any manager of such an organization to consider the use of 
DEA to assist management in improving the productivity of its organization. 

- 23 - 


DEA is a linear programming technique that Is structured as follows: 
Find the set of coefficients u's and v's that will give the highest possible 
efficiency ratio of outputs to inputs for the service unit being evaluated 
(Eg): i.e., the objective function is: 

(la) Maximize E = "l°le '*' "2*^2 

u, 0, + u_0^ + ... u 
1 le z 2e r re 

v. I, + v„I- + ... v I 
1 le 2 2e m me 

(Maximize the efficiency rating E for service unit e) 

subject to the constraint that when the same set of u and v coefficients is 
applied to all other service units being compared, that no service unit will 
be more than 100% efficient as follows: 

Service Unit 1 " l°ll "^ "2°21 '^ ' " "r°re <100% 
^1^11 + ^2^21 + ••• \^ml 

Service Unit 2 " 1^12 ^ "2^22 "^ -' "^ "r°r2 £lOO% 
Vie ■'^2 02e "^ * ' ' + Vm2 


Service Unit e " l°le "^ "2°2e "^ '•• "r"re <100% 

(as in (la)) v^I^^ + v^O^^ + ... v^O^^ 

Service Unit J " l"lj "^ "2°2j "^ •- "^ "r°rj <100% 

^l^lj + ^2^j + ••• + Vmj 

and such that the coefficient values are positive and non-zero. 

v, , . . . V < 
1 r 

u, , . . . u < 0, 
1 m 

The data required to apply DEA is the actual observed outputs produced 
(0^ ••• Of) and actual inputs used (I^^ ... I„,) during one time 
period for each service unit in the set of units that are being evaluated. 
Hence, I^a is the observed amount of the mth input used by the jth service 
unit, and Oj. ^ is the amount of rth output produced by the jth service unit. 

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If the value of Eg for the service unit being evaluated Is less than 
100%, then that unit Is relatively Inefficient and there Is the potential 
for that unit to produce the same level of outputs with fewer Inputs. (See 
[11], [4], [5], and [6] for further details on the theory and application of 

Assume that the DEA evaluation would begin by evaluating the efficiency 
of bank branch B2 . The problem would be structured as follows, based on the 
DEA model above and using the data in table 2: 

Calculate the set of values for uj, v^, V2 that will give B2 the 
highest possible efficiency rating, 

„ , ^ ^ tu(lOOO) [This is the linear program 
Maximize E„™ = I ^v.i ^t c ^t ^ 

^2 v.^(3Q) + V2(200) objective function ] 

subject to the constraint that no service unit can be more than 100% 
efficient when the same values for u^, vj^ and V2 are applied to each 

Bi "i^^QO") <100% 

v^(20) + V2(300) 

B2 "i^^QQQ^ <100% 

Vj^OO) + V2(200) 

B3 "l^^PQO^ <100% 

Vj^CAO) + v^ClOO) 

B4 "l^^QQO) < 100% 

Vj^(20) + V2(200) 

B5 "l^^°°Q^ <100% 

^1^1°^ + ^400) 

and subject to the constraint that v^, V2 and u^ are all greater than 

For B2, DEA calculates its efficiency rating to be 85.7% and the value 
for ui = 1, vj^ = 1.436 and V2 - 0.286. DEA would be rerun for each 
branch in the objective function. 

The results from running DEA fives times with each of the units in the 
ojectlve function is summarized in Table 2. 

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1. Anthony, R. N., and J. S. Reece, Accounting, Text and Cases, sixth 

edition, Homewood, Illinois: Richard D. Iirwln, Inc. 1979, Chapters 
17 and 23. 

2. Sasser, W. F., R. P. Olsen, and D, D. Wyckoff, Management of Service 

Operatlngs, Test, Cases and Readings , Boston, Massachusetts: Allyn 
and Bacon, Inc. 1978. 

3. Anthony, R. N., and R. E. Herzllnger, Management Control In Nonprofit 

Organization, revised edition, Homewood, Illinois: Richard D. 
Irwin, Inc., 1980. 

4. Charnes, A., W. W. Cooper and E. Rhodes, "Measuring the Efficiency of 

Decision Making Units," European Journal of Operations Research, 
Vol. 2, No. 6, November 1974, pp. 429-444. 

3. Charnes, A., W. W. Cooper and E. Rhodes, "Short Communication: 

Measuring Efficiency of Decision Making Units," European Journal of 
Operations Research , Vol. 3, No. 4, July 1979, p. 339. 

6. Charnes, A. W. W. Cooper, and E. Rhodes, "Evaluating Program and 

Magerlal Efficiency: An Application of Data Envelopment Analysis 
to Program Follow Through," Management Science , Vol. 27, No. 6, 
June 1981, pp. 668-697/ 

7. Sherman, H. D., "A New Approach to Evaluate and Measure Hospital 

Efficiency," Sloan School of Management Working Paper #1427-83, 
February 1982. 

8. Bessent, A., W. Bessent, J. Kennlngton, and B. Regan, "An Application of 

Mathematical Programming to Assess Productivity In the Houston 
Independent School District," Management Science , December 1982. 

9. Lewln, A. Y. , and R. C. Morey, "Evaluating Administrative Efficiency of 

Courts," Omega , (forthcoming). 

10. Sherman, H. D. and F. Gold, "Evaluating Operating Efficiency of 

Service Businesses with Data Envelopment Analysis - Empirical Study 
of Bank Branch Operations," Sloan School of Management Working 
Paper #1444-83, June 1983. 

11. Charnes, A., W. W. Cooper and H. D. Sherman, "A Comparative Study of 

Data Envelopment Analysis and Other Approaches to Efficiency 
Evaluation and Estimation," Center for Cybernetic Studies Research 
Report #451, University of Texas at Austin, November 1982. 

i+ 2 2 1 u 3 2 ^ 

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3 TDfiD DDM 511 flM3 

Date Due 



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